PROBLEM SET: Momentum and Conservation of Momentum

AP PHYSICS 1

PROBLEM SET: Momentum and Conservation of Momentum

A.Conceptual Questions

Before beginning read pp. 260-268 in your “College Physics” textbook and answer the following questions on p. 282 # 2,3, 4, 8, 9, 11, 12, 19, 22, and 24.

1)Explain two ways a heavy truck and a person on a skateboard can have the same momentum.

2)In stopping an object, how does the time of impact effect the magnitude of the force used to stop the object?

3)What is the relationship between an impulse on an object and the change in momentum of that object?

4)For a constant force, if the time the force is applied to an object doubles, the impulse will ______.

5)From question #4, by how much is the object’s momentum changed?

6)In a car crash, what is the advantage of an air bag in terms of impulse/change in momentum?

7)Why is the impulse greater on a falling object that bounces instead of an equally massive object that doesn’t bounce?

8)Explain why a tossed egg can be caught with a sagging sheet but not a piece of plywood?

9)A bug and the windshield of a moving car collide. Indicate which of the following statements are TRUE.

The impact force on the bug and the car are the same magnitude.
The impulse on the bug and the car are the same magnitude.
The change in momentum of the bug and the car are the same magnitude.
The change in velocity of the bug and the car are the same.

1) Not moving; truck really slow skateboard really fast. / 2) Small time; big force / 3) The impulse is equal to the change in momentum.
4) double / 5) double / 6) Change in momentum takes place over a longer time period.
7) The bouncing object has two changes in momentum instead of one for the one that doesn’t bounce. / 8) Change in momentum takes longer therefore a smaller force. / 9) a. True
b. True
c. True
d. False

B.Impulse/Change in Momentum Problems

1)A compact car, mass = 725 kg, is moving at 100 km/h.

a)What is the momentum of the car?

b)At what velocity must a larger car, mass = 2175 kg, be traveling in order to have the same momentum?

2)A force of 6.0 N acts on a 3.0 kg object for 10.0 s.

a)What is the object's change in momentum?

b)What is the new velocity of the object if it started at rest?

3)An 1100. kg car moves at 22.0 m/s. Neglecting friction, what breaking force is needed to stop the car in 20.0 s?

4)A net force of 2000. N acts on a rocket of mass 1000. kg. How long must the force be applied in order to increase the rocket's velocity from 10.0 m/s to 200.0 m/s?

5)The velocity of a body of mass m changes by an amount v in a time t. The impulse given to the body is equal to

A.m∆t

D.m∆v.

6)A ball of mass 2.0 kg falls vertically and hits the ground with speed 7.0 m/s as shown below.

beforeafter

The ball leaves the ground with a vertical speed 3.0 m/s. The magnitude of the change in momentum of the ball is _____.

A.zero

B.8.0 Ns

C.10 Ns

D.20 Ns

7)A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface and rebounds to a maximum height at point Y.

Which one of the following graphs best shows the variation with time t of the momentum p of the ball as it moves between point X and point Y?

8)A constant force is applied to a ball of mass m. The velocity of the ball changes from v1 to v2. The impulse received by the ball is

A.m(v2 + v1).

B.m(v2 – v1).

C.m(v22 + v12).

D.m(v22 – v12).

1)20100 kg m/s; 9.26 m/s / 2)60 kg m/s; 20. m/s / 3)–1210 N / 4)95 s / 5)D
6)D / 7)B / 8)B

Determine the total impulse delivered by the force represented by each of the following force versus time graphs. In each case, determine the final velocity of a 5-kg object initially at rest after being acted on by the force indicated in the graph.

1.2.

3.4.

Answers:

1. 2000 N∙s; 400 m/s

2. 8 N∙s; 1.6 m/s

3. 12 N∙s; 2.4 m/s

4. 115 N∙s; 23 m/s

C.Conservation of Linear Momentum Problems

Before beginning read pp. 268-276 in your “College Physics” textbook and answer the following questions on p. 282 # 5, 7, 21, 23, and 25.

9)A 0.105 kg puck moving at 48 m/s is caught by a stationary 75 kg goalie. With what speed does the goalie with the puck slide on the ice?

10)A 35.0 g bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and bullet fly off together at 8.6 m/s. What was the original velocity of the bullet?

11)A 35.0 g bullet moving at 475 m/s strikes a 2.5 kg wooden block. The bullet passes through the block leaving at 275 m/s. If the block was originally at rest, with what velocity is the block moving after the bullet leaves?

12)A green ball (m = 10.0 g) moving with a velocity of 20.0 cm/s catches up to and collides with a red ball (m = 20.0 g) moving along the same line with a velocity of 10.0 cm/s. After the collision, the green ball is still moving in its original direction with a velocity of only 8.0 cm/s. Determine the final velocity of the red ball.

13)Two campers dock a canoe. One camper(80.0 kg) steps onto the dock moving at 4.0 m/s. The canoe and other camper move backwards at 2.9 m/s. If the second camper’s mass is 75.0 kg, what is the mass of the canoe?

14)Two students (90.0 kg and 60.0 kg) on roller skates face-to-face push against each other. The 90.0 kg student moves at 5.0 m/s just after their hands lose contact.

(a)What is the velocity of the other student?

(b)What average force was exerted on each student if they were in contact for 0.003 s?

15)Two spheres of masses m1 and m2 are moving towards each other along the same straight-line with speeds v1 and v2 as shown.

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 − m2v2

D. m2v2 − m1v1

16) The momentum of a system is conserved if _____.

A.no external forces act on the system.

B.no friction forces act within the system.

C.no kinetic energy is lost or gained by the system.

D.the forces acting on the system are in equilibrium.

17) The diagram below shows a trolley of mass 4.0 kg moving on a frictionless horizontal table with a speed of 2.0 m /s. It collides with a stationary trolley also of mass 4.0 kg.

Which of the following diagrams shows a possible outcome?

18)A toy rocket of mass 0.12 kg contains 0.59 kg of water as shown in the diagram below.

The space above the water contains high-pressure air. The nozzle of the rocket has a circular cross-section of radius 1.4 mm. When the nozzle is opened, water emerges from the nozzle at a constant speed of 18 m/ s. The density of water is 1000 kg/ m3.

Deduce that the volume of water ejected per second through the nozzle is 1.1 x 10–4 m3.

Hint:The water is streaming out the entire nozzle, so you can use the full area of the nozzle to determine the volume of water coming out of the nozzle in one second.

Deduce that the upward force that the ejected water exerts on the rocket is approximately 2.0 N. Explain your working by reference to Newton’s laws of motion.

Hint:You will need to make reference to both the second and third laws of motion to receive full marks for your explanation.

Calculate the time delay between opening the nozzle and the rocket achieving lift-off.

Hint:Why would there be a time delay between the water starting to leave the rocket and the rocket taking off? If there is a constant force from the water on the rocket of 2.0 N, at what point will it be strong enough to cause a net upward force on the rocket?

19)A rocket is fired vertically into the air. When the rocket reaches its maximum height, the rocket explodes.

What change, if any, occurs in the momentum and in the kinetic energy of the rocket during the explosion?

momentum / kinetic energy
A. / increases / increases
B. / increases / constant
C. / constant / increases
D. / constant / constant

Hint: Think about what the kinetic energy of the rocket is before the collision and what the kinetic energy of the rocket is after the collision.

9)0.067 m/s
10)1200 m/s
11)2.8 m/s / 12)16 cm/s / 13)35 kg / 14)(a) 7.5 m/s backwards (b) 1.5 x 105 N
15)A / 16)A / 17)A / 18)See end of document for solutions
19)C

D.Elastic & Inelastic Collisions:

20)In an inelastic collision, ______is/are conserved.

21)In a perfectly elastic collision, ______is/are conserved.

22)A 0.015 kg marble moving to the right at 22.5 cm/s collides with a 0.015 kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 18.0 cm/s.

(a)What is the final velocity of the second marble after the collision?

(b)Is the collision elastic or inelastic?

23)A 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target.

a)What is the final velocity of the combined mass?

b)What is the decrease in kinetic energy?

20) momentum / 21) momentum and kinetic energy
22) (a) 22.5 cm/s to the right (b) elastic / 23) (a) 0.43 m/s (b) 17.35 J

E. Conservation of Momentum in Two Dimensions

24)A 1325 kg car moving north at 27.0 m/s collides with a 2165 kg car moving east at 17.0 m/s. The cars stick together when they collide. What is the speed and direction of each car after the collision?

25)A 6 kg object (A) moving at a speed of 3 m/s collides with a 6 kg object (B) at rest. After the collision A moves off in a direction 40˚ to the left of its original path. B moves off in a direction 50˚ to the right of A’s original path. What is the speed of each object after the collision?

26)A stationary billiard ball (mass 0.17 kg) is struck by an identical ball moving at 4 m/s. After the collision the second ball moves off in a direction 60˚ to the left of its original path. The stationary ball moves off in a direction 30˚ to the right of the second ball’s original path. What is the speed of each ball after the collision?

24) 14.7 m/s @ 44.2˚ North of East / 25) A = 2.3 m/s B= 2.0 m/s / 26) 3.5 m/s; 2.0 m/s

Solutions for Problem 18

use of volume = r2v;

=  (1.4  103)2 18;

= 1.1  104 m3

mass ejected per second = 1.1  104 1000 = 0.11kg;

change in momentum per second = 0.11  18;

by Newton’s 2nd, this is force on (ejected) water;

by Newton’s 3rd, equal force acts upwards on rocket;

so force is 2.0N

Do not accept references to momentum conservation.

weight of water to be ejected = 5.0N / mass of water to beejected = 0.51kg;

time delay = 4.6s;